To predict the likelihood of success of a radiotherapeutic strategy, one must be able to assess the effects of irradiation upon both diseased and healthy tissues. This theoretical work explores a method for determining the probability that a healthy organ irradiated non-uniformly will escape complications. Starting with any treatment plan, an N-step dose vs. cumulative-volume histogram for the organ is generated. This is then reduced by means of an interpolation scheme to a slightly different histogram which corresponds to the same overall likelihood of complications, but which contains only N-1 steps. The procedure is repeated until there remains a single-step histogram, for which the complication probability can readily be calculated.